scholarly journals Grouped Normal Variance Mixtures

Risks ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 103
Author(s):  
Erik Hintz ◽  
Marius Hofert ◽  
Christiane Lemieux
Keyword(s):  
Tail Dependence ◽  
R Package ◽  
Normal Mixture ◽  
Multivariate Distributions ◽  
Quasi Monte Carlo ◽  
Fitting Procedure ◽  
Mathematical Expressions ◽  
Mixing Distributions ◽  
Normal Variance ◽  
T Distribution

Grouped normal variance mixtures are a class of multivariate distributions that generalize classical normal variance mixtures such as the multivariate t distribution, by allowing different groups to have different (comonotone) mixing distributions. This allows one to better model risk factors where components within a group are of similar type, but where different groups have components of quite different type. This paper provides an encompassing body of algorithms to address the computational challenges when working with this class of distributions. In particular, the distribution function and copula are estimated efficiently using randomized quasi-Monte Carlo (RQMC) algorithms. We propose to estimate the log-density function, which is in general not available in closed form, using an adaptive RQMC scheme. This, in turn, gives rise to a likelihood-based fitting procedure to jointly estimate the parameters of a grouped normal mixture copula jointly. We also provide mathematical expressions and methods to compute Kendall’s tau, Spearman’s rho and the tail dependence coefficient λ. All algorithms presented are available in the R package nvmix (version ≥ 0.0.5).

scholarly journals Cumulants of Multivariate Symmetric and Skew Symmetric Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1383
Author(s):  
Sreenivasa Rao Jammalamadaka ◽  
Emanuele Taufer ◽  
Gyorgy H. Terdik
Keyword(s):  
Comprehensive Treatment ◽  
Multivariate Distributions ◽  
Symmetric Distributions ◽  
Multivariate T Distribution ◽  
T Distribution ◽  
Multivariate T

This paper provides a systematic and comprehensive treatment for obtaining general expressions of any order, for the moments and cumulants of spherically and elliptically symmetric multivariate distributions; results for the case of multivariate t-distribution and related skew-t distribution are discussed in some detail.

scholarly journals Multivariate fractional phase–type distributions

2020 ◽  
Vol 23 (5) ◽  
pp. 1431-1451 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Martin Bladt ◽  
Mogens Bladt
Keyword(s):  
Tail Dependence ◽  
Jump Process ◽  
Multivariate Distributions ◽  
New Class ◽  
Natural Time ◽  
Special Cases ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Markovian Jump Process ◽  
Heavy Tailed

Abstract We extend the Kulkarni class of multivariate phase–type distributions in a natural time–fractional way to construct a new class of multivariate distributions with heavy-tailed Mittag-Leffler(ML)-distributed marginals. The approach relies on assigning rewards to a non–Markovian jump process with ML sojourn times. This new class complements an earlier multivariate ML construction [2] and in contrast to the former also allows for tail dependence. We derive properties and characterizations of this class, and work out some special cases that lead to explicit density representations.

scholarly journals Pareto Lévy Measures and Multivariate Regular Variation

2012 ◽  
Vol 44 (1) ◽  
pp. 117-138 ◽  
Author(s):  
Irmingard Eder ◽  
Claudia Klüppelberg
Keyword(s):  
Regular Variation ◽  
Lévy Process ◽  
Tail Dependence ◽  
Levy Process ◽  
Dependence Structure ◽  
Lévy Measure ◽  
Multivariate Distributions ◽  
One Dimensional ◽  
The One ◽  
Lévy Measures

We consider regular variation of a Lévy process X := (Xt)t≥0 in with Lévy measure Π, emphasizing the dependence between jumps of its components. By transforming the one-dimensional marginal Lévy measures to those of a standard 1-stable Lévy process, we decouple the marginal Lévy measures from the dependence structure. The dependence between the jumps is modeled by a so-called Pareto Lévy measure, which is a natural standardization in the context of regular variation. We characterize multivariate regularly variation of X by its one-dimensional marginal Lévy measures and the Pareto Lévy measure. Moreover, we define upper and lower tail dependence coefficients for the Lévy measure, which also apply to the multivariate distributions of the process. Finally, we present graphical tools to visualize the dependence structure in terms of the spectral density and the tail integral for homogeneous and nonhomogeneous Pareto Lévy measures.

scholarly journals An Improved Probabilistic Neural Network Model for Directional Prediction of a Stock Market Index

2019 ◽  
Vol 9 (24) ◽  
pp. 5334 ◽  
Author(s):  
Vasana Chandrasekara ◽  
Chandima Tilakaratne ◽  
Musa Mammadov
Keyword(s):  
Stock Market ◽  
Financial Markets ◽  
Financial Market ◽  
Joint Distribution ◽  
Probabilistic Neural Network ◽  
Stock Market Index ◽  
Multivariate Distributions ◽  
Market Index ◽  
Input Variables ◽  
T Distribution

Financial market prediction attracts immense interest among researchers nowadays due to rapid increase in the investments of financial markets in the last few decades. The stock market is one of the leading financial markets due to importance and interest of many stakeholders. With the development of machine learning techniques, the financial industry thrived with the enhancement of the forecasting ability. Probabilistic neural network (PNN) is a promising machine learning technique which can be used to forecast financial markets with a higher accuracy. A major limitation of PNN is the assumption of Gaussian distribution as the distribution of input variables which is violated with respect to financial data. The main objective of this study is to improve the standard PNN by incorporating a proper multivariate distribution as the joint distribution of input variables and addressing the multi-class imbalanced problem persisting in the directional prediction of the stock market. This model building process is illustrated and tested with daily close prices of three stock market indices: AORD, GSPC and ASPI and related financial market indices. Results proved that scaled t distribution with location, scale and shape parameters can be used as more suitable distribution for financial return series. Global optimization methods are more appropriate to estimate better parameters of multivariate distributions. The global optimization technique used in this study is capable of estimating parameters with considerably high dimensional multivariate distributions. The proposed PNN model, which considers multivariate scaled t distribution as the joint distribution of input variables, exhibits better performance than the standard PNN model. The ensemble technique: multi-class undersampling based bagging (MCUB) was introduced to handle class imbalanced problem in PNNs is capable enough to resolve multi-class imbalanced problem persisting in both standard and proposed PNNs. Final model proposed in the study with proposed PNN and proposed MCUB technique is competent in forecasting the direction of a given stock market index with higher accuracy, which helps stakeholders of stock markets make accurate decisions.

scholarly journals Tail Dependence for Heavy-Tailed Scale Mixtures of Multivariate Distributions

2009 ◽  
Vol 46 (4) ◽  
pp. 925-937 ◽  
Author(s):  
Haijun Li ◽  
Yannan Sun
Keyword(s):  
Regular Variation ◽  
Tail Dependence ◽  
Heavy Tail ◽  
Sufficient Condition ◽  
Elliptical Distributions ◽  
Multivariate Regular Variation ◽  
Multivariate Distributions ◽  
Scale Mixtures ◽  
Heavy Tailed ◽  
General Method

The tail dependence of multivariate distributions is frequently studied via the tool of copulas. In this paper we develop a general method, which is based on multivariate regular variation, to evaluate the tail dependence of heavy-tailed scale mixtures of multivariate distributions, whose copulas are not explicitly accessible. Tractable formulae for tail dependence parameters are derived, and a sufficient condition under which the parameters are monotone with respect to the heavy tail index is obtained. The multivariate elliptical distributions are discussed to illustrate the results.

Modeling height-diameter curves for prediction

2015 ◽  
Vol 45 (7) ◽  
pp. 826-837 ◽  
Author(s):  
Lauri Mehtätalo ◽  
Sergio de-Miguel ◽  
Timothy G. Gregoire
Keyword(s):  
Model Fitting ◽  
Tree Height ◽  
R Package ◽  
Nonlinear Functions ◽  
Individual Tree ◽  
Ecological Zones ◽  
Fitting Procedure ◽  
Wide Range ◽  
Fitting Procedures ◽  
Relationship Model

Individual tree heights are needed in many situations, including estimation of tree volume, dominant height, and simulation of tree growth. However, height measurements are tedious compared to tree diameter measurements, and therefore height–diameter (H–D) models are commonly used for prediction of tree height. Previous studies have fitted H–D models using approaches that include plot-specific predictors in the models and those that do not include them. In both these approaches, aggregation of the observations to sample plots has usually been taken into account through random effects, but this has not always been done. In this paper, we discuss four alternative model formulations and report an extensive comparison of 16 nonlinear functions in this context using a total of 28 datasets. The datasets represent a wide range of tree species, regions, and ecological zones, consisting of about 126 000 measured trees from 3717 sample plots. Specific R-functions for model fitting and prediction were developed to enable such an extensive model fitting and comparison. Suggestions on model selection, model fitting procedures, and prediction are given and interpretation of the predictions from different models are discussed. No uniformly best function, model formulation, or model fitting procedure was found. However, a 2-parameter Näslund and Curtis function provided satisfactory fit in most datasets for the plot-specific H–D relationship. Model fitting and height imputation procedures developed for this study are provided in an R-package for later use.

scholarly journals A Generative Model for Correlated Graph Signals

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3078
Author(s):  
Pavel Loskot
Keyword(s):  
Correlation Coefficients ◽  
Generative Models ◽  
Generative Model ◽  
Multivariate Distributions ◽  
Graph Node ◽  
Approximation Accuracy ◽  
Marginal Distributions ◽  
Mathematical Expressions ◽  
Pairwise Correlations ◽  
The Cost

A graph signal is a random vector with a partially known statistical description. The observations are usually sufficient to determine marginal distributions of graph node variables and their pairwise correlations representing the graph edges. However, the curse of dimensionality often prevents estimating a full joint distribution of all variables from the available observations. This paper introduces a computationally effective generative model to sample from arbitrary but known marginal distributions with defined pairwise correlations. Numerical experiments show that the proposed generative model is generally accurate for correlation coefficients with magnitudes up to about 0.3, whilst larger correlations can be obtained at the cost of distribution approximation accuracy. The generative models of graph signals can also be used to sample multivariate distributions for which closed-form mathematical expressions are not known or are too complex.

scholarly journals Tail Dependence for Heavy-Tailed Scale Mixtures of Multivariate Distributions

2009 ◽  
Vol 46 (04) ◽  
pp. 925-937 ◽  
Author(s):  
Haijun Li ◽  
Yannan Sun
Keyword(s):  
Regular Variation ◽  
Tail Dependence ◽  
Heavy Tail ◽  
Sufficient Condition ◽  
Elliptical Distributions ◽  
Multivariate Regular Variation ◽  
Multivariate Distributions ◽  
Scale Mixtures ◽  
Heavy Tailed ◽  
General Method

The tail dependence of multivariate distributions is frequently studied via the tool of copulas. In this paper we develop a general method, which is based on multivariate regular variation, to evaluate the tail dependence of heavy-tailed scale mixtures of multivariate distributions, whose copulas are not explicitly accessible. Tractable formulae for tail dependence parameters are derived, and a sufficient condition under which the parameters are monotone with respect to the heavy tail index is obtained. The multivariate elliptical distributions are discussed to illustrate the results.

scholarly journals Estimating Cross-Classified Population Counts of Multidimensional Tables: An Application to Regional Australia to Obtain Pseudo-Census Counts

2017 ◽  
Vol 33 (4) ◽  
pp. 1021-1050 ◽  
Author(s):  
Thomas Suesse ◽  
Mohammad-Reza Namazi-Rad ◽  
Payam Mokhtarian ◽  
Johan Barthélemy
Keyword(s):  
Census Data ◽  
R Package ◽  
Family Type ◽  
Likelihood Method ◽  
Estimation Methods ◽  
Iterative Proportional Fitting ◽  
Marginal Population ◽  
Fitting Procedure ◽  
Australian Census ◽  
Population Counts

AbstractEstimating population counts for multidimensional tables based on a representative sample subject to known marginal population counts is not only important in survey sampling but is also an integral part of standard methods for simulating area-specific synthetic populations. In this article several estimation methods are reviewed, with particular focus on the iterative proportional fitting procedure and the maximum likelihood method. The performance of these methods is investigated in a simulation study for multidimensional tables, as previous studies are limited to 2 by 2 tables. The data are generated under random sampling but also under misspecification models, for which sample and target populations differ systematically. The empirical results show that simple adjustments can lead to more efficient estimators, but generally, at the expense of increased bias. The adjustments also generally improve coverage of the confidence intervals. The methods discussed in this article along with standard error estimators, are made freely available in the R packagemipfp. As an illustration, the methods are applied to the 2011 Australian census data available for the Illawarra Region in order to obtain estimates for the desired three-way table for age by sex by family type with known marginal tables for age by sex and for family type.

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